A block of mass mblock = 1.9 kg rests on a cart of mass mcart = 3.9 kg, which mo

Question

A block of mass mblock = 1.9 kg rests on a cart of mass mcart = 3.9 kg, which moves without friction on a horizontal surface. The coefficient of static friction between the block and the cart is ? = 0.74. The cart is accelerating to the right. What is the maximum acceleration such that the block does not slide on the cart? amax = m / s2 What is the magnitude of the force on the cart required to provide the acceleration amax?

Explanation / Answer

Since the cart is horizontal Normal force = the weight of the block= 1.9 * 9.8=18.62 the force of friciton between the block and the cart = Normal force * coifisint of the friction = 18.62 *0.74= 13.78 N in this case Force of friction also equals to = Mass *acceleration => acceleration = Force of friction / Mass = =13.78 /1.9= 0.72 m/s^2 The force needed to accelerate the cart and the block =acceleration * Combined mass = 0.72 *(1.9+3.9)=4.2 N

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